Wolfgang Pauli

How to use this course

Wolfgang Pauli is remembered by chemists for one rule: no two electrons in an atom share the same quantum state. That rule explains the periodic table, the rigidity of solids and the stability of stars. Physicists know him for much more. He wrote the standard account of relativity at twenty-one, introduced the spin matrices, solved hydrogen in the new quantum mechanics, predicted the neutrino and proved that spin decides statistics. His letters and his criticism shaped the work of a whole generation.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. The lessons follow his work in order: relativity (1921), atomic structure and spin (1924–1927), the neutrino (1930), and quantum field theory (1929–1955). Formulas use SI units unless a lesson says otherwise; in Lessons 09 and 10 we set \(\hbar=c=1\).

Timeline

Vienna, 1900–1918

Wolfgang Ernst Pauli was born in Vienna on 25 April 1900. His father, also named Wolfgang, had been born Wolfgang Pascheles in Prague, trained as a physician and became a research chemist and professor at the University of Vienna, working on colloids and proteins. He had changed the family name and converted from Judaism to Catholicism before his son was born. Pauli’s mother, Bertha Camilla Schütz, was a journalist and writer, and his younger sister Hertha Pauli became an actress and author.

The physicist and philosopher Ernst Mach was his godfather, and the boy’s middle name honours him. Pauli later said that Mach’s influence on the household was strong, and that he received from it an anti-metaphysical outlook. Mach gave him a silver cup at his christening.

At the Döblinger Gymnasium Pauli was bored, and he read physics under his desk. By the end of school he had mastered Albert Einstein’s general theory of relativity, published only in 1915–16. He graduated with distinction in July 1918, a few months before the end of the war. His first paper, on the energy of the gravitational field in general relativity, appeared shortly afterwards.

Munich and the relativity article, 1918–1921

In autumn 1918 Pauli went to the University of Munich to study theoretical physics with Arnold Sommerfeld, the most successful teacher of theorists of his day. Sommerfeld soon treated him as a colleague. In 1919 he gave Pauli a task he had accepted himself: the article on relativity for the Encyklopädie der mathematischen Wissenschaften, the great German encyclopaedia edited under Felix Klein.

Pauli, still a student, wrote a monograph of 237 pages. It covered the special theory, the general theory, Hermann Weyl’s and Arthur Eddington’s unified theories, and the experimental evidence, with a critical command of the literature. It appeared in 1921, the year of his doctorate. Einstein reviewed it with open admiration, writing that no one studying it would guess it was the work of a man of twenty-one. The article was reprinted as a book and, with Pauli’s added notes, translated into English in 1958. It is still in print.

Quantum theory and the thesis

Munich in these years was the centre of the old quantum theory of Niels Bohr and Sommerfeld, in which electron orbits are selected by quantum conditions. In Sommerfeld’s seminar Pauli met Werner Heisenberg, who arrived in 1920 and became his closest scientific friend and sparring partner. For his doctorate Pauli applied the old quantum theory to the hydrogen molecular ion \(\mathrm H_2^+\), one electron bound to two protons. The calculation was a tour de force, and it gave the wrong binding energy. Pauli concluded correctly that the failure lay in the theory, which could not handle systems more complex than hydrogen. He received his doctorate summa cum laude in July 1921.

Göttingen, Copenhagen, Hamburg, 1921–1928

In the winter semester of 1921–22 Pauli was assistant to Max Born at Göttingen. Born found him brilliant and a poor fit as an assistant, since Pauli worked at night and rarely appeared before late morning. After a short period at Hamburg with Wilhelm Lenz, Pauli accepted Niels Bohr’s invitation to Copenhagen for 1922–23. There he worked on the anomalous Zeeman effect, the splitting of spectral lines in a magnetic field into patterns that the orbit models could not explain. He later recalled walking the streets of Copenhagen in despair over the problem.

In 1923 he moved to the University of Hamburg, where he became Privatdozent. His six Hamburg years were the most productive of his life. In 1924 he suggested that atomic nuclei carry angular momentum, which accounted for hyperfine structure. Late that year he found the exclusion principle (Lesson 05), published in 1925. In 1926 he solved hydrogen in Heisenberg’s new matrix mechanics (Lesson 07), and in 1927 he gave the spin of the electron its mathematical form (Lesson 06). At Hamburg he worked alongside the experimental physicist Otto Stern.

He was also becoming the critic whom physicists both feared and needed. Early in 1925 Ralph Kronig told him the idea of a spinning electron, and Pauli dismissed it; Kronig did not publish. When George Uhlenbeck and Samuel Goudsmit proposed spin later that year, Pauli objected again, until Llewellyn Thomas showed in 1926 that a relativistic correction removed the factor-of-two discrepancy in the fine structure. Pauli accepted spin, and within a year he had written its theory.

Relativity in covariant form

For the general reader. Pauli’s encyclopaedia article taught a generation to write physics so that its form does not depend on the observer. Electric and magnetic fields mix when you change your state of motion, but certain combinations of them stay the same for everyone. Finding those combinations is the first exercise in thinking relativistically.

Four-vectors and the field tensor

Use coordinates \(x^\mu=(ct,\mathbf x)\) and the metric \(\eta=\mathrm{diag}(1,-1,-1,-1)\). A Lorentz transformation \(\Lambda\) preserves \(\eta\): \(\Lambda^\mathsf T\eta\Lambda=\eta\). The potentials form a four-vector \(A^\mu=(\phi/c,\mathbf A)\), and the field tensor is \(F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu\), with \(F^{0i}=-E^i/c\) and \(F^{ij}=-\epsilon^{ijk}B^k\). Maxwell’s equations become

with \(J^\nu=(c\rho,\mathbf J)\). The second set holds identically once \(F\) comes from a potential. Both sides transform as tensors, so the equations hold in every inertial frame.

Sketch. Contracting with \(\eta\) gives \(F_{\mu\nu}F^{\mu\nu}=2\sum_{i<j}(F_{ij})^2-2\sum_i(F_{0i})^2=2(B^2-E^2/c^2)\). For the second, \(F_{\mu\nu}\tilde F^{\mu\nu}\) is linear in each of \(\mathbf E\) and \(\mathbf B\) and rotation invariant, so it is a multiple of \(\mathbf E\cdot\mathbf B\); evaluating one component fixes the constant. Any other scalar is a function of these two, because the combination \(\mathbf E/c+i\mathbf B\) transforms under the Lorentz group as a complex vector under \(\mathrm{SO}(3,\mathbb C)\), whose only invariant is its complex square \((E^2/c^2-B^2)+2i\,\mathbf E\cdot\mathbf B/c\).

Weyl’s theory

In 1918 Weyl proposed a geometry in which the length of a vector changes under parallel transport by a factor \(\exp\!\big(\int\varphi_\mu dx^\mu\big)\), and identified \(\varphi_\mu\) with the electromagnetic potential. Einstein objected that the frequency of an atomic clock would then depend on its history, so that sharp spectral lines could not exist. Pauli’s article set out this objection carefully, together with his own view that a field theory should only use quantities that are in principle observable. Weyl’s idea survived in another form: after quantum mechanics the factor became a phase \(e^{ie\int A_\mu dx^\mu/\hbar}\), and gauge invariance became the principle that fixes the coupling of charged matter to light.

The exclusion principle

For the general reader. Why are atoms not all alike, with every electron sitting in the lowest orbit? Pauli’s answer of 1925 was a rule: each quantum state can hold at most one electron. Electrons are forced to stack into higher and higher shells, and the pattern of filled and partly filled shells is the periodic table. Matter is solid because electrons refuse to crowd together.

The problem

In the old quantum theory an electron in an atom had three quantum numbers: the principal number \(n\), the orbital number \(l\) and the magnetic number \(m_l\). Bohr had explained the periodic table in 1922 by assigning electrons to shells with capacities 2, 8, 18 and 32, but he had no rule that produced those numbers. The anomalous Zeeman effect posed a second puzzle. The magnetic splitting of the alkali lines required half-integer quantum numbers and a magnetic factor (the Landé \(g\)-factor) that no orbital model gave.

Late in 1924 Pauli argued that the closed inner shells carry no angular momentum, so the anomalies belong to the valence electron itself. He gave the electron a fourth quantum number, with two values, describing a property he called a two-valuedness not describable classically. At the same time Edmund Stoner showed that the number of electrons in a closed subshell equals the number of Zeeman levels of an alkali atom with the same \(n\) and \(l\). Pauli saw the general rule.

Capacities 2, 8, 18, 32 follow at once. The lengths of the periods, 2, 8, 8, 18, 18, 32, 32, come from the same subshell counts once one knows the order in which subshells fill in many-electron atoms (\(4s\) before \(3d\), and so on), which is set by screening of the nuclear charge.

The modern form

In 1926 Heisenberg and Paul Dirac recast the principle in wave mechanics. The wave function of \(N\) identical electrons must be antisymmetric under exchange of any two, including their spin labels:

For independent electrons in orbitals \(\psi_1,\dots,\psi_N\), the antisymmetric state is the Slater determinant \(\Psi=\frac{1}{\sqrt{N!}}\det[\psi_a(x_b)]\). If two orbitals coincide, two rows are equal and \(\Psi=0\). Pauli’s rule is the special case of independent particles. Enrico Fermi and Dirac drew the statistical consequences in 1926: Fermi–Dirac statistics, which Pauli himself used in 1927 to explain the weak, temperature-independent paramagnetism of metals.

Much later, Freeman Dyson and Andrew Lenard proved (1967) that ordinary matter is stable, with energy bounded below by a constant times the number of particles, only because electrons obey the exclusion principle. Elliott Lieb and Walter Thirring gave a much shorter proof in 1975.

Spin, Pauli matrices, the Pauli equation

For the general reader. An electron behaves as if it were a tiny magnet with two possible orientations. In 1927 Pauli showed how to describe this in quantum mechanics: the wave function gets two components, and three small matrices, now called the Pauli matrices, act on them. The same matrices describe every two-state quantum system, including the qubits of a quantum computer.

The algebra

The spin operator is \(\mathbf S=\frac\hbar2\boldsymbol\sigma\). The commutators show that \(\mathbf S\) satisfies the angular-momentum algebra, and \(S^2=\frac34\hbar^2\) gives spin \(\tfrac12\). The matrices \(-\frac i2\sigma_j\) span the Lie algebra \(\mathfrak{su}(2)\), and the rotation by angle \(\theta\) about the unit vector \(\mathbf n\) acts on spinors by

The Pauli equation (1927)

For a particle of charge \(q\) and mass \(m\) in potentials \((\phi,\mathbf A)\), let \(\boldsymbol\pi=\mathbf p-q\mathbf A\) with \(\mathbf p=-i\hbar\nabla\). Pauli’s Hamiltonian acts on two-component wave functions \(\psi=(\psi_\uparrow,\psi_\downarrow)\):

Derivation. Apply the identity above with \(\mathbf a=\mathbf b=\boldsymbol\pi\); the components of \(\boldsymbol\pi\) do not commute, but the identity still holds in the form \((\boldsymbol\sigma\cdot\boldsymbol\pi)^2=\boldsymbol\pi^2+i\boldsymbol\sigma\cdot(\boldsymbol\pi\times\boldsymbol\pi)\). Acting on a function \(\psi\),

so \(i\boldsymbol\sigma\cdot(\boldsymbol\pi\times\boldsymbol\pi)=-q\hbar\,\boldsymbol\sigma\cdot\mathbf B\). For the electron, \(q=-e\), the spin term is \(-\boldsymbol\mu\cdot\mathbf B\) with \(\boldsymbol\mu=-g\frac{e}{2m}\mathbf S\) and \(g=2\). Pauli inserted the magnetic moment by hand in 1927; writing the kinetic term as \((\boldsymbol\sigma\cdot\boldsymbol\pi)^2\) shows that \(g=2\) is natural, and Dirac’s relativistic equation of 1928 produced it automatically. The Pauli equation is the nonrelativistic limit of the Dirac equation.

Hydrogen from matrix mechanics

For the general reader. In 1925 Heisenberg invented a new quantum mechanics made of arrays of numbers, but nobody could yet use it on a real atom. Within weeks Pauli derived the energy levels of hydrogen from it by an algebraic trick. He used a hidden conserved quantity of Kepler orbits, the vector that points to the closest approach of the orbit. This convinced many physicists that the new theory was right, before Erwin Schrödinger’s wave equation appeared.

The classical vector

For \(H=\frac{p^2}{2m}-\frac{k}{r}\), with \(k=\frac{e^2}{4\pi\varepsilon_0}\), the angular momentum \(\mathbf L=\mathbf r\times\mathbf p\) and the vector \(\mathbf A=\mathbf p\times\mathbf L-mk\,\hat{\mathbf r}\) are constant. \(\mathbf A\) points to the perihelion and \(|\mathbf A|=mk\varepsilon\), with \(\varepsilon\) the eccentricity. Its constancy is why Kepler orbits close.

Pauli’s quantum version (1926)

In quantum mechanics \(\mathbf p\times\mathbf L\ne-\mathbf L\times\mathbf p\), so Pauli symmetrized: \(\mathbf A=\frac12(\mathbf p\times\mathbf L-\mathbf L\times\mathbf p)-mk\,\hat{\mathbf r}\). It commutes with \(H\), and satisfies

On a bound eigenspace with energy \(E<0\), set \(\mathbf M=\mathbf A/\sqrt{-2mE}\). Then

the commutation relations of \(\mathfrak{so}(4)\cong\mathfrak{su}(2)\oplus\mathfrak{su}(2)\).

Derivation. Let \(\mathbf J_\pm=\frac12(\mathbf L\pm\mathbf M)\). Each satisfies the \(\mathfrak{su}(2)\) relations and they commute with each other. Because \(\mathbf L\cdot\mathbf M=0\), \(\mathbf J_+^2=\mathbf J_-^2=\frac14(\mathbf L^2+\mathbf M^2)\), so both have the same spin \(j\in\{0,\frac12,1,\dots\}\). The relation for \(\mathbf A^2\) becomes \(\mathbf L^2+\mathbf M^2+\hbar^2=-\frac{mk^2}{2E}\). Hence

With \(n=2j+1\) this is the Bohr formula. The eigenspace carries the representation \((j,j)\) of dimension \((2j+1)^2=n^2\), and decomposing it under \(\mathbf L=\mathbf J_++\mathbf J_-\) gives \(l=0,1,\dots,2j=n-1\). Vladimir Fock explained the symmetry geometrically in 1935: in momentum space the bound states are harmonics on the three-sphere.

The neutrino

For the general reader. In beta decay a nucleus emits an electron, and the electrons come out with a whole range of energies. Energy seemed to disappear. Bohr was ready to give up energy conservation. In 1930 Pauli proposed instead that an invisible, neutral, very light particle carries off the missing energy. It took twenty-six years to detect one.

Two crises

James Chadwick showed in 1914 that the electrons of beta decay have a continuous spectrum. Calorimetric measurements by Charles Ellis and William Wooster in 1927 confirmed that the average energy deposited was well below the maximum, so the missing energy was not simply lost in the detector. There was a second problem. Before the neutron, nuclei were thought to contain protons and electrons. The nitrogen-14 nucleus would then hold 14 protons and 7 electrons, an odd number of spin-\(\tfrac12\) particles, and should obey Fermi statistics. Band spectra of the \(\mathrm N_2\) molecule showed that it obeys Bose statistics.

On 4 December 1930 Pauli addressed an open letter to the “radioactive ladies and gentlemen” meeting at Tübingen, which included Lise Meitner and Hans Geiger. He proposed, as a desperate remedy, that nuclei contain neutral spin-\(\tfrac12\) particles of small mass, emitted together with the electron in beta decay. He called them neutrons. After Chadwick discovered the heavy neutron in 1932, Fermi renamed Pauli’s particle the neutrino, and in 1933–34 built his theory of beta decay on it.

Proof. In the two-body case \(\mathbf p_1=-\mathbf p_2\). Squaring the four-momentum relation \(P-p_1=p_2\) gives \(M^2c^2-2ME_1+m_1^2c^2=m_2^2c^2\), which fixes \(E_1\). With three bodies, the remaining two particles can share any invariant mass between \(m_2+m_3\) and \(M-m_1\), and \(E_1\) varies with it.

Detection

In 1956 Frederick Reines and Clyde Cowan observed inverse beta decay, \(\bar\nu_e+p\to n+e^+\), in a detector beside the Savannah River nuclear reactor, and telegraphed Pauli. Pauli’s particle is now one of three neutrino flavours, and the discovery of neutrino oscillations, which requires neutrino masses, was recognized by the Nobel Prize of 2015.

Quantized fields and spin–statistics

For the general reader. Some particles, such as electrons, refuse to share a state; others, such as photons, crowd together, and lasers depend on it. Is this a separate law of nature, or does it follow from something deeper? In 1940 Pauli proved that it follows from relativity and causality. Particles with half-integer spin must be loners, and particles with integer spin must be gregarious.

Field quantization

In two papers of 1929 and 1930 Heisenberg and Pauli gave a general canonical formalism for quantizing a relativistic field theory from its Lagrangian, and applied it to electrodynamics. In 1934 Pauli and Victor Weisskopf quantized the charged Klein–Gordon field. The resulting theory had particles of both charges with positive energy, and so produced antiparticles without Dirac’s sea of negative-energy electrons. Pauli called it, with some pleasure, the anti-Dirac paper.

For a free complex scalar field (with \(\hbar=c=1\))

where \(a\) destroys particles and \(b^\dagger\) creates antiparticles. With commutators \([a_{\mathbf k},a_{\mathbf k'}^\dagger]=[b_{\mathbf k},b_{\mathbf k'}^\dagger]=(2\pi)^3 2\omega_k\,\delta^3(\mathbf k-\mathbf k')\), the Hamiltonian is a sum of positive terms, and

where the Pauli–Jordan function \(\Delta\) vanishes for spacelike \(x-y\).

Sketch for spin 0. Suppose instead that \(\{a_{\mathbf k},a_{\mathbf k'}^\dagger\}\) and \(\{b_{\mathbf k},b_{\mathbf k'}^\dagger\}\) take the canonical values. Then \(\{\phi(x),\phi^\dagger(y)\}=\Delta^{(1)}(x-y)\), the even solution of the Klein–Gordon equation, which does not vanish at spacelike separation. Bilinear observables such as the charge density would then fail to commute at spacelike separation, violating causality. Sketch for spin \(\tfrac12\). For the Dirac field the Hamiltonian takes the form \(\sum\omega_k(a^\dagger a-b\,b^\dagger)\). With commutators, \(b\,b^\dagger=b^\dagger b+\text{const}\), so \(H\) contains \(-\omega_k b^\dagger b\) and is unbounded below. With anticommutators, \(-b\,b^\dagger=b^\dagger b-\text{const}\), and the energy is bounded below. Markus Fierz, Pauli’s assistant, gave the first proof in 1939 for arbitrary spin; Pauli’s 1940 paper in Physical Review organized the argument around these two requirements. Rigorous proofs within axiomatic field theory came from Gerhart Lüders, Bruno Zumino and Nicholas Burgoyne in 1958.

Regularization and the CPT theorem

For the general reader. After the war, quantum electrodynamics produced infinities that had to be tamed. Pauli and Felix Villars gave a clean way to do it: add fictitious heavy particles that cancel the infinities and then let their mass go to infinity. A few years later Pauli proved that any reasonable quantum field theory looks the same if you reverse time, reflect space and swap particles with antiparticles all at once.

Pauli–Villars regularization (1949)

A scalar propagator \(\frac{1}{k^2-m^2}\) falls like \(k^{-2}\), and loop integrals over \(d^4k\) diverge. Pauli and Villars replaced it by

which falls like \(k^{-4}\). The subtracted term is the propagator of a heavy particle with the wrong sign of its norm. In general one adds regulator fields with masses \(M_i\) and coefficients \(c_i\), with \(c_0=1\), \(M_0=m\) for the physical field, chosen so that \(\sum c_i=0\) and \(\sum c_iM_i^2=0\), make the photon self-energy finite while preserving gauge invariance and Lorentz invariance. At the end one lets \(M_i\to\infty\) and absorbs the dependence on \(\log M_i\) into the physical charge and mass. The method was used throughout the renormalization of quantum electrodynamics.

The CPT theorem

Let \(C\) exchange particles and antiparticles, \(P\) reflect space and \(T\) reverse time. Lüders proved in 1954, and Pauli proved more generally in 1955 in a volume for Bohr’s seventieth birthday, that their product is always a symmetry. John Stewart Bell found a proof independently, and Res Jost gave an axiomatic one in 1958.

Idea of the proof. In the complexified Lorentz group the transformation \(x\mapsto-x\) is connected to the identity: a rotation by \(\pi\) in the \(x^0x^1\) plane followed by one in the \(x^2x^3\) plane, after continuing the boost angle to imaginary values. Correlation functions of a local theory are analytic in this complex domain, so their invariance under the real Lorentz group extends to \(x\mapsto-x\). Turning that into an antiunitary operator on states requires reversing the order of operators, which brings in the spin–statistics signs and the charge conjugation.

In January 1957 experiments led by Chien-Shiung Wu, and by Leon Lederman and Richard Garwin, showed that the weak interaction violates \(P\) and \(C\) separately. Pauli had expected nature to respect parity, and was surprised. CPT survived intact, and the theorem became the framework in which the discrete symmetries are now discussed.

Zurich, crisis and Princeton, 1928–1946

In April 1928 Pauli became professor of theoretical physics at the ETH in Zurich, succeeding Peter Debye. He held the chair until his death. His institute became a meeting point of quantum physics, and his assistants form a roll of honour: Ralph Kronig, Felix Bloch, Rudolf Peierls, Hendrik Casimir, Victor Weisskopf, Markus Fierz, Res Jost, Felix Villars and, last of all, Charles Enz. His doctoral students included Enz and Max Robert Schafroth. His criticism was famous for its bluntness; a weak paper might be judged “not even wrong”. Students and colleagues also spoke, half seriously, of the Pauli effect, the tendency of experiments to fail when he entered the room.

Crisis and Jung

His private life fell apart at the end of the 1920s. His mother died in the late 1920s. He married the dancer Käthe Deppner in December 1929, and they divorced within a year. He drank heavily. In January 1932 he consulted the psychiatrist Carl Gustav Jung, who referred him to a younger colleague and later worked with Pauli’s dreams himself. The relationship became a long intellectual exchange about archetypes, symmetry and the place of the observer. In 1934 Pauli married Franca Bertram, and the marriage lasted until his death.

The Second World War

The annexation of Austria in 1938 made Pauli a German citizen, and under the Nazi racial laws he counted as Jewish because of his grandparents. An application for Swiss citizenship was refused. In the summer of 1940 he left Europe for the Institute for Advanced Study in Princeton, where he stayed until 1946 and worked with Einstein, John von Neumann and visiting physicists. In November 1945 he learned that he had won the Nobel Prize in Physics, “for the discovery of the Exclusion Principle, also called the Pauli Principle”. Einstein, who had nominated him, spoke at a celebration at the Institute. Pauli became an American citizen in 1946 and returned to Zurich the same year. He gave his Nobel lecture in Stockholm on 13 December 1946.

Last years, death, legacy, 1946–1958

After the war Pauli received the honours of an elder statesman: Swiss citizenship on 25 July 1949, the Franklin Medal in 1952, Foreign Membership of the Royal Society in 1953, the Matteucci Medal in 1956 and the Max Planck Medal in 1958. In 1952 he and Jung published a joint volume, translated as The Interpretation of Nature and the Psyche, with Pauli’s essay on the archetypal ideas behind Johannes Kepler’s science.

His last major physics project was a unified nonlinear spinor field theory with Heisenberg. In early 1958 Heisenberg presented it to the press with great confidence. Pauli, after a lecture tour in the United States, concluded that it did not work and withdrew from it publicly. In December 1958 he fell ill in Zurich. He died of pancreatic cancer in the Red Cross Hospital on 15 December 1958, aged 58. The story that his hospital room was number 137, a number that fascinated him because \(1/\alpha\approx137\), is often told.

Legacy

• Atomic and condensed-matter physics: the exclusion principle underlies the periodic table, chemical bonding, the band theory of solids and the stability of matter; Pauli paramagnetism is a basic effect of metals.
• Quantum theory: the Pauli matrices are the language of spin and of qubits; his 1933 Handbuch article on the general principles of wave mechanics was a standard reference for decades.
• Particle physics: the neutrino, the spin–statistics theorem and the CPT theorem are pillars of the Standard Model.
• Correspondence: his scientific letters, edited by Karl von Meyenn in several volumes, are a major source for the history of twentieth-century physics. The Pauli Archive is held at CERN.

Connections

People linked to Wolfgang Pauli across this collection. A name without a link has no page here yet. See Wolfgang Pauli in the network of all 337 lives →

Teachers and advisors

• Arnold Sommerfeld 1918-1921
• Niels Bohr

Students

• Charles Enz
• Felix Bloch
• Hendrik Casimir
• Max Robert Schafroth
• Ralph Kronig
• Res Jost
• Rudolf Peierls

Influenced by

• Ernst Mach
• Hermann Weyl
• James Chadwick

Influenced

• Enrico Fermi
• J. Robert Oppenheimer 1928-1929

Colleagues and collaborators

• Albert Einstein 1940-1946
• Erwin Schrödinger
• Hermann Weyl
• Lise Meitner
• Max Born 1921-1922
• Niels Bohr 1922-1958
• Paul Dirac
• Peter Debye
• Subrahmanyan Chandrasekhar
• Werner Heisenberg 1920-1958
• Felix Villars 1949
• Gerhart Lüders
• Markus Fierz
• Otto Stern 1923-1928
• Victor Weisskopf 1934
• Wilhelm Lenz 1922-1928

Rivals

• Louis de Broglie

Friends

• Erich Hecke
• Ernst Mach
• Harish-Chandra
• Carl Gustav Jung 1932-1958

Also mentioned in this life

• Charles-Augustin de Coulomb
• Christian Doppler
• Arthur Eddington
• Benjamin Franklin
• Hans Geiger
• Paul Gordan
• Johannes Kepler
• Felix Klein
• Pierre-Simon Laplace
• Sophus Lie
• Hendrik Antoon Lorentz
• James Clerk Maxwell
• Max Planck
• John von Neumann

Fields

• theoretical physics 11 lives
• quantum mechanics 6 lives
• quantum field theory 4 lives
• relativity 3 lives

On CoursesHub

• Quantum Mechanics
• Quantum Field Theory
• Particle Physics

Sources and further reading

Biography

1. J. J. O’Connor and E. F. Robertson, Wolfgang Pauli, MacTutor History of Mathematics.
2. Wolfgang Pauli, Wikipedia.
3. CERN Archive, Pauli Archive biographical record.
4. C. P. Enz, Wolfgang Pauli, 1900–1958, Europhysics News 31 (2000).
5. C. P. Enz, No Time to be Brief: A Scientific Biography of Wolfgang Pauli, Oxford University Press, 2002.
6. The Nobel Prize in Physics 1945, NobelPrize.org (with the Nobel lecture, “Exclusion principle and quantum mechanics”).
7. C. A. Meier (ed.), Atom and Archetype: The Pauli/Jung Letters, 1932–1958, Princeton University Press, 2001.
8. K. von Meyenn (ed.), Wolfgang Pauli: Wissenschaftlicher Briefwechsel, Springer, 1979–2005.

Physics

1. W. Pauli, Relativitätstheorie, Encyklopädie der mathematischen Wissenschaften V.19 (1921); English translation Theory of Relativity, Pergamon, 1958.
2. W. Pauli, Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren, Z. Phys. 31 (1925) 765–783.
3. W. Pauli, Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik, Z. Phys. 36 (1926) 336–363.
4. W. Pauli, Zur Quantenmechanik des magnetischen Elektrons, Z. Phys. 43 (1927) 601–623.
5. W. Heisenberg and W. Pauli, Zur Quantendynamik der Wellenfelder, Z. Phys. 56 (1929) 1–61.
6. W. Pauli and V. Weisskopf, Über die Quantisierung der skalaren relativistischen Wellengleichung, Helv. Phys. Acta 7 (1934) 709–731.
7. W. Pauli, The connection between spin and statistics, Phys. Rev. 58 (1940) 716–722.
8. W. Pauli and F. Villars, On the invariant regularization in relativistic quantum theory, Rev. Mod. Phys. 21 (1949) 434–444.
9. W. Pauli, Exclusion principle, Lorentz group and reflection of space-time and charge, in Niels Bohr and the Development of Physics, Pergamon, 1955.
10. L. M. Brown, The idea of the neutrino, Physics Today 31(9) (1978) 23–28.
11. I. Duck and E. C. G. Sudarshan, Pauli and the Spin-Statistics Theorem, World Scientific, 1997.
12. Spin–statistics theorem and CPT symmetry, Wikipedia (historical sections).